Related rates of $y^2-3xy+x^2=25$ given $x$ and $y$ are dependent of $t$

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I am given the following problem:

Two variables $x$ and $y$ are dependent of $t$ and are related according to

$$y^2-3xy+x^2=25$$

If $x$ varies $1$ unit when $x = 0$ then find $\frac{dy}{dt}$ at that specific moment.

What I have so far is

$$ 2y \frac{dy}{dt} - 3y \frac{dx}{dt} - 3x \frac{dy}{dt} + 2x \frac{dx}{dt} = 0\\ 2y \frac{dy}{dt} - 3y = 0\\ \frac{dy}{dt} = \frac{3}{2} $$

Is that correct? Did I miss something?

Thank you.